===[http://gicl.cs.drexel.edu/wiki-data/images/5/5c/TheMechanismOfLocomotionINSnakes.pdf The Mechanism of Locomotion in Snakes]===

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5. Serpentine, concertina, and crotaline movements do not depend on active movements on the part of the ribs or scales. Rectilinear movement involving these structures has not been observed in Tropidonotus.

5. Serpentine, concertina, and crotaline movements do not depend on active movements on the part of the ribs or scales. Rectilinear movement involving these structures has not been observed in Tropidonotus.

Snake robots may one day play a crucial role in search and rescue operations and fire-fighting where it may either be too narrow or to dangerous for personnel to operate. Properties such as high terrainability, redundancy, and the possibility of complete sealing of the body of the robot, make snake robots very interesting for practical applications and hence as a research topic. During the last ten to fifteen years, the published literature on snake robots has increased vastly. However, no thorough review of the theory presented in this period regarding mathematical modeling techniques and locomotion of snake robots has been found. The purpose of this paper is to give such a review. Both purely kinematic models and models including dynamics are investigated. The choice of modeling method is linked to snake robot design characteristics and locomotion approach. Different approaches to biologically inspired locomotion are also discussed

Snake robots may one day play a crucial role in search and rescue operations and fire-fighting where it may either be too narrow or to dangerous for personnel to operate. Properties such as high terrainability, redundancy, and the possibility of complete sealing of the body of the robot, make snake robots very interesting for practical applications and hence as a research topic. During the last ten to fifteen years, the published literature on snake robots has increased vastly. However, no thorough review of the theory presented in this period regarding mathematical modeling techniques and locomotion of snake robots has been found. The purpose of this paper is to give such a review. Both purely kinematic models and models including dynamics are investigated. The choice of modeling method is linked to snake robot design characteristics and locomotion approach. Different approaches to biologically inspired locomotion are also discussed

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===[http://gicl.cs.drexel.edu/wiki-data/images/f/fc/AnalysisAndDesignOfAMulti-LinkMobileRobot%28Serpentine%29.pdf Analysis and design of a multi-link mobile robot (Serpentine)]===

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# Analysis and design of a multi-link mobile robot (Serpentine)

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Abstract:

Abstract:

This paper is a study on dynamic behavior of a snake robot, called Serpentine robot, 2nd version (SR#2). The SR#2 is the latest version of snake robots developed at FIBO as a research platform for studying serpentine gaits. The gait is in form of sinusoidal curve, considered one of the most effectiveness crawling pattern in the natural world. The Active Cord Mechanism (ACM) assumption, initiated by Hirose, is implemented. The robot motion results from different joint torques and frictional reacting forces in each wheel. In this study, we proposed a modified serpeniod function with steering command to control the robot's direction. We also performed dynamic analysis using Kane's method. Holonomic constraints under frictional forces and nonholonomic constraints unders velocities were considered. We verified our algorithm for directional control on this Serpentine robot both simulation and experiment.

This paper is a study on dynamic behavior of a snake robot, called Serpentine robot, 2nd version (SR#2). The SR#2 is the latest version of snake robots developed at FIBO as a research platform for studying serpentine gaits. The gait is in form of sinusoidal curve, considered one of the most effectiveness crawling pattern in the natural world. The Active Cord Mechanism (ACM) assumption, initiated by Hirose, is implemented. The robot motion results from different joint torques and frictional reacting forces in each wheel. In this study, we proposed a modified serpeniod function with steering command to control the robot's direction. We also performed dynamic analysis using Kane's method. Holonomic constraints under frictional forces and nonholonomic constraints unders velocities were considered. We verified our algorithm for directional control on this Serpentine robot both simulation and experiment.

This paper considers the problem of serpentine, or snake-like, locomotion from the perspective of geometric mechanics. A particular model based on Hirose's active cord mechanism is analyzed. Using the kinematic constraints, we develop a connection, which describes the net motion of the machine as a function of variations in the mechanism's shape variables. We present simulation results demonstrating three types of locomotive gaits, one of which bears an obvious resemblance to the serpentine motion of a snake. We also discuss how these algorithms can be used to optimize certain inputs given the particular choice of physical parameters for a snake robot

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===[http://gicl.cs.drexel.edu/wiki-data/images/e/e8/AnalysisOfCreepingLocomotionOFASnakeRobotOnASlope.pdf Analysis of creeping locomotion of a snake robot on a slope]===

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Biological snakes' diverse locomotion modes and physiology make them supremely adapted for environment. To realize these snakes' noticeable features, we have developed a snake-like robot that has no any forward direction driving force. To enlarge the environment-adaptable ability of our robot, in this study we discuss the creeping locomotion of our snake-like robot on a slope. A computer simulator is presented for analysis of the creeping locomotion of our snake-like robot on a slope, and the environment-adaptable body shape for the creeping locomotion of the snake-like robot on slope is also derived through this simulator.

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===Analysis of Creeping Locomotion of a Snake-Like Robot (No free full text)===

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Snakes perform many kinds of movement adapted to the environment. Utilizing the snake (its forms and motion) as a model to develop a snake-like robot, that performs the snake's function, is important for generating a new type of locomotion and expanding the possible uses of robots. In this study, we developed a simulator to simulate the creeping locomotion of the snake-like robot, in which the robot dynamics is modeled and the interaction with the environment is considered through Coulomb friction. This simulator makes it possible to analyze creeping locomotion with normaldirection slip, adding to the glide along the tangential direction. Through the developed simulator, we investigate the snake-like robot creeping locomotion which is generated only by swinging each of the joints from side to side and discuss the optimal creeping locomotion of the snake-like robot that is adapted to the environment.

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===[http://gicl.cs.drexel.edu/wiki-data/images/4/45/TurningAndSideMotionOfSnake-LikeRobot.pdf Turning and side motion of snake-like robot]===

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With high adaptability to environments snake-like robots offer a variety of advantages over other mobile robots. Such a robot with passive wheels has quite different mechanism in locomotion from that of other locomotion systems. We have developed a snake-like robot for rescue applications. The unit composing the snake-like robot of Shenyang Institute of Automation (SIA) is a module including actuating system and control system. To let the snake-like robot perform turning motion and compensate offset and orientation errors of the robot, we propose an amplitude modulation method and a phase modulation method based on analysis of the serpenoid curve. The side motion of the snake-like robot can also be generated by the amplitude modulation. The tracking control method is also proposed based on sensor information. Computer simulations and experimental tests are performed to show the validity of the proposed methods.

The authors describe a snake robot without wheels and develop its model based on the directional friction coefficients. After the model transformation that decouples the inertial locomotion from the internal shape motion, an optimally efficient serpentine locomotion is investigated. Based on the analysis results, a velocity control scheme is proposed using a quasi-linearizing input transformation, and its validity is demonstrated by a laboratory experiment with a five-link serpentine robot. The results reported here focus on the planar serpentine gait that is suited for locomotion in an environment where friction with directional preference cna be realized. (CSA)

This paper describes our research project on snake-like locomotion of robotic platforms and the results of the experiments conducted with a wheel-less snake-like robot prototype. Biological inspiration has been at the hardcore of the mechanical design and the control method applied to the robot. With closed-loop control applied to the present wheel-less prototype, it has succeeded in progressing through lateral undulation, the most common limbless locomotion type observed in natural snakes. Main results consist of the robustness of the locomotion with respect to the variations in initial conditions and external perturbations

A non-smooth 3D mathematical model of the dynamics of a snake robot (without wheels) is developed in this paper. The model is based on the framework of non-smooth dynamics and convex analysis which allows us to easily incorporate unilateral contact forces and friction forces based on Coulomb's law of dry friction. Impact and stick-slip transitions are modeled as instantaneous. A numerical integrator on impulse-velocity level, the time-stepping method, is used for simulation, which helps avoid an explicit switch between equations of motion during simulation. Numerical results are presented for a snake robot with 26 degrees of freedom and 22 possible contact points along its body. Simulation results of the snake motion pattern `lateral undulation' are shown.

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===[http://gicl.cs.drexel.edu/wiki-data/images/8/83/LocomotionControlOFASnake-LikeRobotBasedOnDynamicManipulability.pdf Locomotion control of a snake-like robot based on dynamic manipulability]===

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We discuss autonomous locomotion control of a snake-like articulated robot with passive wheels. Such a robot has a quite different mechanism in locomotion from that of other locomotion systems, namely, it has no driving wheel and moves only by bending its body. Hence the locomotability depends on its posture. In order to evaluate the locomotability, we utilize a notion of dynamic manipulability which has been applied to a robot manipulator. We also propose a simple controller based on this manipulability. Simulation results show that a certain periodic winding motion is automatically generated

A common view in snake robot research is that serpentine locomotion is only possible when there is nonuniform friction. This paper demonstrates that this view is incorrect, through a simple and easily reproducible experiment. We also present a theoretical kinematical analysis, which explains the experiment.

Polychaete annelid worms provide a biological paradigm of versatile locomotion and effective motion control, adaptable to a large variety of unstructured environmental conditions (water, sand, mud, sediment, etc.). The undulatory locomotion of their segmented body is characterized by the combination of a unique form of tail-to-head body undulations, with the rowing-like action of numerous lateral appendages distributed along their body. Computational models of polychaete-like crawling and swimming have been developed, based on the Lagrangian dynamics of the system and on resistive models of its interaction with the environment, and used for simulation studies demonstrating the generation of undulatory gaits. Several lightweight robotic prototypes have been developed, whose undulatory actuation achieves propulsion on sand. Extensive experiments demonstrate that the propulsion of these robots is characterized by essential features of polychaete locomotion, in agreement with the corresponding simulations.

1. Of the four main types of locomotion observed in snakes, three (serpentine, concertina and crotaline) can be elicited from the common grass snake (Tropidonotus natrix) by appropriate modification of the animal's environment.

2. Serpentine motion depends on three factors, (i) The body must be thrown into one or more curves each of which exhibits an increase of curvature when measured towards the head of the animal, (ii) Active muscular tension must develop in the axial muscles which lie on the same side of the body as that in which the curvature is increasing, (iii) The body must be subjected to at least three external resistances acting normally to the surface of the body. The propulsive force is the resultant of the reactions exercised by all these external resistances.

3. A snake cannot propel itself by serpentine movement along a straight or circular path. Under such conditions Tropidonotus progresses by concertina movements, the nature of which are described.

4. The muscular cycle of a snake exhibiting ‘crotaline’, or side-winding, movements is essentially the same as that during serpentine motion; the difference in the type of movement relative to the ground is due to a difference in the nature of the external resistances offered by the animal's environment. The mechanical principle of crotaline movement is, fundamentally, that of a caterpillar tractor.

5. Serpentine, concertina, and crotaline movements do not depend on active movements on the part of the ribs or scales. Rectilinear movement involving these structures has not been observed in Tropidonotus.

Snake robots may one day play a crucial role in search and rescue operations and fire-fighting where it may either be too narrow or to dangerous for personnel to operate. Properties such as high terrainability, redundancy, and the possibility of complete sealing of the body of the robot, make snake robots very interesting for practical applications and hence as a research topic. During the last ten to fifteen years, the published literature on snake robots has increased vastly. However, no thorough review of the theory presented in this period regarding mathematical modeling techniques and locomotion of snake robots has been found. The purpose of this paper is to give such a review. Both purely kinematic models and models including dynamics are investigated. The choice of modeling method is linked to snake robot design characteristics and locomotion approach. Different approaches to biologically inspired locomotion are also discussed

This paper is a study on dynamic behavior of a snake robot, called Serpentine robot, 2nd version (SR#2). The SR#2 is the latest version of snake robots developed at FIBO as a research platform for studying serpentine gaits. The gait is in form of sinusoidal curve, considered one of the most effectiveness crawling pattern in the natural world. The Active Cord Mechanism (ACM) assumption, initiated by Hirose, is implemented. The robot motion results from different joint torques and frictional reacting forces in each wheel. In this study, we proposed a modified serpeniod function with steering command to control the robot's direction. We also performed dynamic analysis using Kane's method. Holonomic constraints under frictional forces and nonholonomic constraints unders velocities were considered. We verified our algorithm for directional control on this Serpentine robot both simulation and experiment.

This paper considers the problem of serpentine, or snake-like, locomotion from the perspective of geometric mechanics. A particular model based on Hirose's active cord mechanism is analyzed. Using the kinematic constraints, we develop a connection, which describes the net motion of the machine as a function of variations in the mechanism's shape variables. We present simulation results demonstrating three types of locomotive gaits, one of which bears an obvious resemblance to the serpentine motion of a snake. We also discuss how these algorithms can be used to optimize certain inputs given the particular choice of physical parameters for a snake robot

Biological snakes' diverse locomotion modes and physiology make them supremely adapted for environment. To realize these snakes' noticeable features, we have developed a snake-like robot that has no any forward direction driving force. To enlarge the environment-adaptable ability of our robot, in this study we discuss the creeping locomotion of our snake-like robot on a slope. A computer simulator is presented for analysis of the creeping locomotion of our snake-like robot on a slope, and the environment-adaptable body shape for the creeping locomotion of the snake-like robot on slope is also derived through this simulator.

Analysis of Creeping Locomotion of a Snake-Like Robot (No free full text)

Abstract:

Snakes perform many kinds of movement adapted to the environment. Utilizing the snake (its forms and motion) as a model to develop a snake-like robot, that performs the snake's function, is important for generating a new type of locomotion and expanding the possible uses of robots. In this study, we developed a simulator to simulate the creeping locomotion of the snake-like robot, in which the robot dynamics is modeled and the interaction with the environment is considered through Coulomb friction. This simulator makes it possible to analyze creeping locomotion with normaldirection slip, adding to the glide along the tangential direction. Through the developed simulator, we investigate the snake-like robot creeping locomotion which is generated only by swinging each of the joints from side to side and discuss the optimal creeping locomotion of the snake-like robot that is adapted to the environment.

With high adaptability to environments snake-like robots offer a variety of advantages over other mobile robots. Such a robot with passive wheels has quite different mechanism in locomotion from that of other locomotion systems. We have developed a snake-like robot for rescue applications. The unit composing the snake-like robot of Shenyang Institute of Automation (SIA) is a module including actuating system and control system. To let the snake-like robot perform turning motion and compensate offset and orientation errors of the robot, we propose an amplitude modulation method and a phase modulation method based on analysis of the serpenoid curve. The side motion of the snake-like robot can also be generated by the amplitude modulation. The tracking control method is also proposed based on sensor information. Computer simulations and experimental tests are performed to show the validity of the proposed methods.

The authors describe a snake robot without wheels and develop its model based on the directional friction coefficients. After the model transformation that decouples the inertial locomotion from the internal shape motion, an optimally efficient serpentine locomotion is investigated. Based on the analysis results, a velocity control scheme is proposed using a quasi-linearizing input transformation, and its validity is demonstrated by a laboratory experiment with a five-link serpentine robot. The results reported here focus on the planar serpentine gait that is suited for locomotion in an environment where friction with directional preference cna be realized. (CSA)

This paper describes our research project on snake-like locomotion of robotic platforms and the results of the experiments conducted with a wheel-less snake-like robot prototype. Biological inspiration has been at the hardcore of the mechanical design and the control method applied to the robot. With closed-loop control applied to the present wheel-less prototype, it has succeeded in progressing through lateral undulation, the most common limbless locomotion type observed in natural snakes. Main results consist of the robustness of the locomotion with respect to the variations in initial conditions and external perturbations

In this paper we extend a non-smooth 3D mathe-
matical model of a snake robot to also include external obstacles
to enable obstacle aided locomotion. The model is based on the
framework of non-smooth dynamics and convex analysis. This
framework enables us to systematically and easily incorporate
unilateral contact forces (from the obstacles and the ground) and
isotropic friction forces based on Coulomb’s law. The obstacles
are shaped as vertical cylinders and we describe the contact
between a link of the snake robot and an obstacle with a single,
moving contact point. Hence, the effect of the link touching the
obstacle is accurately described. Simulation results for a 11 link
snake robot moving by the serpentine motion pattern ‘lateral
undulation’ while pushing against obstacles are given.

A non-smooth 3D mathematical model of the dynamics of a snake robot (without wheels) is developed in this paper. The model is based on the framework of non-smooth dynamics and convex analysis which allows us to easily incorporate unilateral contact forces and friction forces based on Coulomb's law of dry friction. Impact and stick-slip transitions are modeled as instantaneous. A numerical integrator on impulse-velocity level, the time-stepping method, is used for simulation, which helps avoid an explicit switch between equations of motion during simulation. Numerical results are presented for a snake robot with 26 degrees of freedom and 22 possible contact points along its body. Simulation results of the snake motion pattern `lateral undulation' are shown.

We discuss autonomous locomotion control of a snake-like articulated robot with passive wheels. Such a robot has a quite different mechanism in locomotion from that of other locomotion systems, namely, it has no driving wheel and moves only by bending its body. Hence the locomotability depends on its posture. In order to evaluate the locomotability, we utilize a notion of dynamic manipulability which has been applied to a robot manipulator. We also propose a simple controller based on this manipulability. Simulation results show that a certain periodic winding motion is automatically generated

A common view in snake robot research is that serpentine locomotion is only possible when there is nonuniform friction. This paper demonstrates that this view is incorrect, through a simple and easily reproducible experiment. We also present a theoretical kinematical analysis, which explains the experiment.

Polychaete annelid worms provide a biological paradigm of versatile locomotion and effective motion control, adaptable to a large variety of unstructured environmental conditions (water, sand, mud, sediment, etc.). The undulatory locomotion of their segmented body is characterized by the combination of a unique form of tail-to-head body undulations, with the rowing-like action of numerous lateral appendages distributed along their body. Computational models of polychaete-like crawling and swimming have been developed, based on the Lagrangian dynamics of the system and on resistive models of its interaction with the environment, and used for simulation studies demonstrating the generation of undulatory gaits. Several lightweight robotic prototypes have been developed, whose undulatory actuation achieves propulsion on sand. Extensive experiments demonstrate that the propulsion of these robots is characterized by essential features of polychaete locomotion, in agreement with the corresponding simulations.